Conversely, several works have studied regularisers that push apart embeddings [1]}, [2]}, [3]}, [4]};
e.g.,
under the assumption that embeddings are normalised,
the spreadout regulariser [1]} is
\(M_1 = \frac{1}{|\lbrace x \ne x^{\prime }\rbrace |}\sum _{x \ne x^{\prime }}\Phi ( x )^\top \Phi ( x^{\prime } ) \\M_2 = \frac{1}{|\lbrace x \ne x^{\prime }\rbrace |} \sum _{x^{\prime } \ne x} ( \Phi ( x )^\top \Phi ( x^{\prime } ) )^2 \\\Omega _{\rm spread}( x, y ) \stackrel{.}{=}M_1^2 + \max \left(0, M_2 - \frac{1}{d}\right).\) 
